Let a Markov chain \(X_1,X_2,\cdots \)  on a state space \(\mathcal {S}\)  with transition kernel \(Q(x,dy)\) , where \(\mathcal {S}\)  is a Polish space in \(\mathbb {R}\) . In this paper, we consider the Markov chains which are irreducible and recurrent, so the existence of a stationary distribution is guaranteed. An irreducible and recurrent Markov chain on an infinite state-space is called Harris chain [1]}. A Markov chain is called reversible if there exists a probability measure \(\pi \)  on \(\mathcal {S}\)  satisfying the detailed balance conditions,
\(\pi (dx)Q(x,dy)=\pi (dy)Q(y,dx),\qquad \forall x, y \in \mathcal {S}.\) 
